We consider the following one- and two-dimensional bucketing problems: Given a set S of n points in ℝ1 or ℝ2 and a positive integer b, distribute the points of S into b equal-size buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n/b) + △ points lies in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and △. No prior knowledge of △ is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of 0(b4△2 log n + n). For the two-dimensional problem, we present a Monte-Carlo algorithm that runs in sub-quadratic time for certain values of b and △. The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω(n2) time in the worst case even for constant values of b and △.
CITATION STYLE
Agarwal, P. K., Bhattacharya, B. K., & Sen, S. (1999). Output-sensitive algorithms for uniform partitions of points. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1741, pp. 403–414). Springer Verlag. https://doi.org/10.1007/3-540-46632-0_41
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